Question

Сколько сторон у правильного n-угольника если его внутренний угол 135°?

Answer 1

(n-2)*180/n=135
180n-135n=360
45n=360
n=8 углов и 8 сторон

Answer 2

Number of Sides in a Regular n-gon with an Internal Angle of 135°

A regular polygon is a polygon with all sides and angles equal. To determine the number of sides in a regular n-gon with an internal angle of 135°, we can use the formula:

n = 360° / x

where n is the number of sides and x is the internal angle of the polygon.

In this case, the internal angle is 135°. Plugging this value into the formula, we get:

n = 360° / 135°

Simplifying the equation, we have:

n = 8/3

Therefore, a regular polygon with an internal angle of 135° has approximately 8/3 sides. However, since a polygon cannot have a fractional number of sides, we need to round this value to the nearest whole number.

Rounding 8/3 to the nearest whole number, we get:

n ≈ 3

Therefore, a regular polygon with an internal angle of 135° has approximately 3 sides.

Please note that this approximation is based on rounding the value of 8/3 to the nearest whole number. The exact number of sides may vary depending on the specific context or mathematical interpretation.